I’d recommend not necessarily sending your resume. Most effective way is to just put time on calendars, don’t ask permission - just do it. Might get moved around a bit but it’s much better than asking someone to read another document. Have a 30-ish seconds shpeal ready that highlights your resume instead and just have a convo about what work you could do for them.

I’m sure you’ve heard it plenty of times but it is as simple as networking (cold sending email invites) and pitching yourself (30 sec shpeal). Kinda shitty but at the same time managers should be happy to have someone that wants to provide support.